Primary biliary cirrhosis (PBC) is a disease of unknown cause in which the small bile ducts in the liver are destroyed slowly by inflammation. Most physicians believe that PBC is due to an abnormal immune response directed against the bile ducts in the liver. It is considered to be an autoimmune disease. Loss of bile ducts causes bile to back up in the liver and ultimately leads to liver damage, liver cirrhosis and possibly liver failure. There is no known specific treatment for PBC at present. UDCA and methotrexate may be useful in the treatment of this autoimmune disease. This study will examine whether treatment with UDCA and methotrexate is better than treatment with UDCA alone.